Examples for the use are scores of the same set of student in
different exams, or repeated sampling from the same units. The
test measures whether the average score differs significantly
across samples (e.g. exams). If we observe a large p-value, for
example greater than 0.05 or 0.1 then we cannot reject the null
hypothesis of identical average scores. If the p-value is smaller
than the threshold, e.g. 1%, 5% or 10%, then we reject the null
hypothesis of equal averages. Small p-values are associated with
large t-statistics.